Ito-Wentzell-Lions formula for measure dependent random fields under full and conditional measure flows

Goncalo dos Reis; Vadim Platonov

doi:10.1007/s11118-022-10012-1

Ito-Wentzell-Lions formula for measure dependent random fields under full and conditional measure flows

Goncalo dos Reis, Vadim Platonov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We present several It\^o-Wentzell formulae on Wiener spaces for real-valued functional random field of It\^o type depending on measures. We distinguish the full- and the marginal-measure flow cases. Derivatives with respect to the measure components are understood in the sense of Lions.

Original language	English
Pages (from-to)	1313-1344
Journal	Potential analysis
Volume	59
Early online date	31 May 2022
DOIs	https://doi.org/10.1007/s11118-022-10012-1
Publication status	Published - 31 Oct 2023

Keywords / Materials (for Non-textual outputs)

math.PR
math.FA
60H05 (Primary), 60H10, 60H15 (Secondary)

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10.1007/s11118-022-10012-1Licence: Creative Commons: Attribution (CC-BY)

Ito_Wentzell_Lions_v05_0___POTA__final_Accepted author manuscript, 385 KB

https://arxiv.org/abs/1910.01892

Cite this

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title = "Ito-Wentzell-Lions formula for measure dependent random fields under full and conditional measure flows",

abstract = " We present several It\textbackslash{}\textasciicircum{}o-Wentzell formulae on Wiener spaces for real-valued functional random field of It\textbackslash{}\textasciicircum{}o type depending on measures. We distinguish the full- and the marginal-measure flow cases. Derivatives with respect to the measure components are understood in the sense of Lions. ",

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AU - Reis, Goncalo dos

AU - Platonov, Vadim

N1 - 28 pages

PY - 2023/10/31

Y1 - 2023/10/31

N2 - We present several It\^o-Wentzell formulae on Wiener spaces for real-valued functional random field of It\^o type depending on measures. We distinguish the full- and the marginal-measure flow cases. Derivatives with respect to the measure components are understood in the sense of Lions.

AB - We present several It\^o-Wentzell formulae on Wiener spaces for real-valued functional random field of It\^o type depending on measures. We distinguish the full- and the marginal-measure flow cases. Derivatives with respect to the measure components are understood in the sense of Lions.

KW - math.PR

KW - math.FA

KW - 60H05 (Primary), 60H10, 60H15 (Secondary)

U2 - 10.1007/s11118-022-10012-1

DO - 10.1007/s11118-022-10012-1

M3 - Article

SN - 0926-2601

VL - 59

SP - 1313

EP - 1344

JO - Potential analysis

JF - Potential analysis

ER -

Ito-Wentzell-Lions formula for measure dependent random fields under full and conditional measure flows

Abstract

Keywords / Materials (for Non-textual outputs)

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